1. Field of the Invention
The present invention relates to a design support method and design support program suitable for achieving an optimum design of a conveying path by analyzing a behavior of a sheet-shaped member such as a paper by using simulation when the sheet-shaped member is conveyed in an apparatus such as a copying machine and the like.
2. Related Background Art
In designing a conveying path, it is preferable that functions of a designed object are examined under various conditions before the object is actually manufactured because the number of manufacturing and testing steps for trial manufacture of the object can be reduced and a developing time period and a developing cost can be reduced. As techniques for simulating the behavior of the paper in the conveying path by means of a computer for such a purpose, design support systems as disclosed in Japanese Patent Application Laid-open Nos. H11-195052 (1999) and H11-116133 (1999) have been proposed. This technique is a design support system in which a conveying resistance and contact angles between a flexible medium and guides are evaluated by representing the flexible medium as a finite element by means of a finite element method and by judging contact conditions between the flexible medium and guides and/or rollers in the conveying path and by solving a motion equation numerically.
Further, as described in a document “The Japan Society of Mechanical Engineers International Journal (JSME International Journal)” (written by KAZUSI YOSHIDA; 96-1530, C(1997), 230-236 pages), a technique in which a calculation speed is enhanced by representing the flexible medium by mass and spring more simply has been disclosed.
The motion of the flexible medium is solved by numerical value time integration. That is to say, the motion of the flexible medium is solved by forming a motion equation of the flexible medium represented by the finite element or a mass-spring system separately and by dividing an analysis subject time into time steps having finite widths and by calculating acceleration, speed and displacement which are unknown values successively for each time step from a time 0. As techniques for solving the movement of the flexible medium, a NEWMARK β method, a WILLSON θ method, an Euler method, a KUTTA-MERSON method and the like are well known.
Further, for example, a technique described in a document “The Japan Society of Mechanical Engineers International Journal (JSME International Journal)” (written by NORIAKI OKAMOTO et. al; 67-654, C(2001), 185-192 pages) is also known. This technique is a contact structure analysis technique, using a finite element model, for calculating a fluctuation rate regarding a denomination value of a conveying speed caused by deformation of an elastic material such as a roller under pressure.
According to this technique, a roller is deformed as shown in FIG. 16 by a pressure force. A portion of the roller 81 subjected to pressure caused by the contact between the roller and a paper P is called as a nip portion 82 and the paper as a flexible medium is contacted with the roller 81 and conveyed at the nip portion 82. The roller 81 is being driven in a direction shown by the arrow a. When the roller 81 is rotated by Δø as shown in FIG. 17, a shifting amount (arrow Lo) of a periphery of the roller at a non-deformed point remote from the nip portion becomes R×Δø (where, R is a radius of the roller).
However, at the nip portion 82, since the surface of the roller is stretched in a circumferential direction as shown by the arrow b, even when the roller is rotated by the same amount of Δø, a shifting amount (arrow Ln) of the surface of the roller becomes greater than the above-mentioned value. Accordingly, the conveying speed becomes faster by an amount corresponding to the elongation of the roller in the nip portion. This speed fluctuation rate is varied with parameters such as a thickness, hardness and a pressure force of the roller and the like.
Further, the shape of the nip portion 82 is also varied with the above-mentioned parameters of a pair of rollers 81 and 83. In the example shown in FIG. 16, the thickness of rubber of the roller 81 is greater than that of the roller 83 and the hardness of the roller 81 is substantially equal to that of the roller 83. The radii R of both rollers 81 and 83 are the same. Accordingly, the shape of the nip portion 82 is convex toward an upward direction and is like an arc having a radius greater than the radius R of the roller.
As a result, when the paper P is being conveyed by the roller 81, a posture of the paper directs along substantially tangential lines with respect to curves near both ends of the nip portion, as shown by the arrow 84a at the inlet of the nip portion and the arrow 84b at the outlet. Accordingly, the posture of the paper in the nip portion is changed in accordance with the shape of the nip portion.
In the above-mentioned design support program, a user can set a speed for conveying the flexible medium by inputting design values of the rollers. However, the speed of the roller for conveying the flexible medium may not be determined in a meaning manner from the radius and the rotation speed of the roller. In this case, in the actual designing, the target conveying speed of the roller may not be obtained and unexpected tensioning and great slack are caused between the pair of rollers to jam the paper, thereby causing a defect image.
Further, the change in the posture of the flexible medium in the nip portion between the rollers cannot be estimated, so that an introducing direction of the flexible medium into the nip portion and a guiding direction of the flexible medium from the nip may become improper to trap the flexible medium, thereby causing the paper jam.
The speed fluctuation of the roller is caused by the fact that the elastic material such as rubber constituting the roller is deformed by the pressure force to change the peripheral length of the roller nip portion. Further, the change in posture of the flexible medium in the nip portion is caused by the fact that the shape of the elastic material is changed by the pressure force. Amounts of the change in the peripheral length and the change in the shape are determined by factors such as material and hardness of the roller, thickness of the rubber layer, load and the like and, thus, it is difficult to specify these amount values from a simple calculation equation.
There was a need for performing, with higher accuracy, behavior simulation such as elongation and slack in the flexible medium, trapping of the flexible medium before and after the rollers and the like, by estimating such speed fluctuation and posture change.
In the prior art, the speed fluctuation rate caused by the elastic deformation of the rollers can be estimated by contact structure analysis using the finite element model.
However, if the contact structure analysis is applied to the whole conveying path including the elastic deformation of the rollers, it takes a long time to manufacture the model and to perform the calculations, so that there arose a problem that the incorporation of the contact structure analysis into the design support program for supporting the design of the conveying path is not practical.